2) Consider the following simple and rather unrealistic mathematical model of a network. Each of n vertices belongs to one of several groups. The m-th group has n, vertices and each vertex in that group is connected to others in the group with independent probability Pm = A(n, -1) , where A and B are constants, but not to any vertices in other groups. Thus, this network takes the form of a set of disjoint clusters or communities (20 pts). a. Calculate the expected degree (k) of a vertex within group m. b. Calculate the expected value of C,, of the local clustering coefficient for vertices within group m. c. Show that C, oc (k) (1-) d. What value would B have to have for the expected value of the local clustering to fall off with increasing degree as (k)